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Class 10

Explore popular questions from Introduction to Trigonometry for Class 10. This collection covers Introduction to Trigonometry previous year Class 10 questions hand picked by experienced teachers.

Introduction to Trigonometry

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Q 1. If {tex} \sin \theta + \cos \theta = \sqrt { 2 } \cos \left( 90 ^ { \circ } - \theta \right) {/tex} then {tex} \cot \theta {/tex} is equal to

A

{tex} \frac { 1 } { \sqrt { 2 } } {/tex}

B

{tex} \frac { \sqrt { 3 } } { 2 } {/tex}

C

{tex} \frac { 1 } { \sqrt { 2 } - 1 } {/tex}

{tex} \sqrt { 2 } - 1 {/tex}

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Q 2. If {tex} \sec \theta + \tan \theta = x {/tex} then the value of {tex} \sec \theta - \tan \theta {/tex} is equal to

A

{tex} - x {/tex}

{tex} \frac { 1 } { x } {/tex}

C

{tex} - \frac { 1 } { x } {/tex}

D

{tex} \sqrt { x } {/tex}

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Q 3. If {tex} \mathrm { x } = \mathrm { a } \sin \theta {/tex} and {tex} \mathrm { y } = \mathrm { b } \cos \theta , {/tex} then the value of {tex} \mathrm { b } ^ { 2 } \mathrm { x } ^ { 2 } + \mathrm { a } ^ { 2 } \mathrm { y } ^ { 2 } {/tex} is

{tex} \mathrm{a ^ { 2 } b ^ { 2 }} {/tex}

B

{tex}\mathrm{ a b} {/tex}

C

{tex} \mathrm{\frac { 1 } { a ^ { 2 } b ^ { 2 } }} {/tex}

D

{tex} \mathrm {\frac { 1 } { \mathrm { ab } }} {/tex}

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Q 4. An equation is called an identity if

If is true for all values of variable

B

Not for all values of variabls but some value of variable

C

Exactly one value of variables

D

Exactly two value of variables

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Q 5. If {tex} x = ( \sec A + \tan A ) ( \sec B + \tan B ) ( \sec C + \tan C ) \& y = ( \sec A - \tan A ) ( \sec B + \tan B ) ( \sec C + \tan C ) {/tex} and {tex} x = y {/tex} then {tex} x \& y {/tex} is equal to

{tex} \pm 1 {/tex}

B

{tex}0{/tex}

C

{tex} \pm 2 {/tex}

D

None of these

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Q 6. If {tex} x = \cot ^ { 2 } \theta - \frac { 1 } { \sin ^ { 2 } \theta } {/tex} than the value of {tex} x {/tex} is

A

{tex} 1 {/tex}

{tex} - 1 {/tex}

C

{tex} \pm 1 {/tex}

D

zero

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Q 7. {tex} 2 \left( \sin ^ { 6 } \theta + \cos ^ { 6 } \theta \right) - 3 \left( \sin ^ { 4 } \theta + \cos ^ { 4 } \theta \right) {/tex} is equal

A

zero

B

1

-1

D

None of these

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Q 8. {tex} \sqrt { \frac { 1 + \sin \theta } { 1 - \sin \theta } } {/tex} is equal to

{tex} \sec \theta + \tan \theta {/tex}

B

{tex} \sec \theta - \tan \theta {/tex}

C

{tex} \sec ^ { 2 } \theta + \tan ^ { 2 } \theta {/tex}

D

{tex} \sec ^ { 2 } \theta - \tan ^ { 2 } \theta {/tex}

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Q 9. {tex} \sec ^ { 4 } A - \sec ^ { 2 } A {/tex} is equal to

A

{tex} \tan ^ { 2 } A - \tan ^ { 4 } A {/tex}

B

{tex} \tan ^ { 4 } A - \tan ^ { 2 } A {/tex}

{tex} \tan ^ { 4 } A + \tan ^ { 2 } A {/tex}

D

{tex} \tan ^ { 2 } A + \tan ^ { 4 } A {/tex}

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Q 10. {tex} \cos ^ { 4 } A - \sin ^ { 4 } A {/tex} is equal to

A

{tex} 2 \cos ^ { 2 } A + 1 {/tex}

{tex} 2 \cos ^ { 2 } A - 1 {/tex}

C

{tex} 2 \sin ^ { 2 } - 1 {/tex}

D

{tex} 2 \sin ^ { 2 } A + 1 {/tex}

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Q 11. {tex} \mathrm { P } = ( 1 + \cot \theta - \cosec \theta ) ( 1 + \tan \theta + \sec \theta ) {/tex}
the value of {tex}\mathrm P {/tex} is equal to

A

1

2

C

4

D

zero

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Q 12. {tex} ( \cosec \theta - \sin \theta ) ( \sec \theta - \cos \theta ) ( \tan \theta + \cot \theta ) {/tex} is equal to

A

zero

1

C

-1

D

none of these

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Q 13. The value of is equal to:

A

{tex} \sqrt { 3 } {/tex}

{tex} - \sqrt { 3 } {/tex}

C

{tex} \frac { 1 } { \sqrt { 3 } } {/tex}

D

{tex} - \frac { 1 } { \sqrt { 3 } } {/tex}

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Q 14. The expression {tex} \sqrt { \sin ^ { 2 } ( 37.5 ) ^ { \circ } + \cos ^ { 2 } ( 37.5 ) ^ { \circ } } + \sqrt { \cos ^ { 2 } ( 37.5 ) ^ { \circ } + sin ^ { 2 } ( 37.5 ) ^ { \circ } } {/tex} simplifies to:

A

an irrational number

B

a prime number

a natural number which is not composite

D

a real number of the form {tex} a + \sqrt { b } {/tex}

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Q 15. If {tex} 15 \sin ^ { 4 } \alpha + 10 \cos ^ { 4 } \alpha = 6 , {/tex} then the value of {tex}8 \cosec ^ { 4 } \alpha + 27 \sec ^ { 6 } \alpha {/tex} is

A

200

250

C

220

D

None of these

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Q 16. If {tex} a = \frac { \cot \theta } { \cot \theta - \cot 3 \theta }\ \ \& \ b = \frac { \tan \theta } { \tan \theta - \tan 3 \theta } {/tex} then {tex} \sqrt { a + b } {/tex} is equal to

A

{tex} \pm 2 {/tex}

B

{tex} - 2 {/tex}

{tex} + 1 {/tex}

D

{tex} - 1 {/tex}

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Q 17. If {tex} a \cos \theta - b \sin \theta = C {/tex} then {tex} a \sin \theta + b \cos \theta = {/tex}

A

{tex} \pm \sqrt { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } } {/tex}

{tex} \pm \sqrt { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } {/tex}

C

{tex} \pm \sqrt { c ^ { 2 } - a ^ { 2 } - b ^ { 2 } } {/tex}

D

None of these

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Q 18. If {tex} a \cos \theta + b \sin \theta = 4 {/tex} and {tex} a \sin \theta - b \cos \theta = 3 {/tex} then {tex} \left( a ^ { 2 } + b ^ { 2 } \right) {/tex} is equal to

A

7

B

12

25

D

None of these

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Q 19. If {tex} \cos A = \frac { 4 } { 5 } {/tex} then the value of {tex} \tan A {/tex} is :

A

{tex} \frac { 3 } { 5 } {/tex}

{tex} \frac { 3 } { 4 } {/tex}

C

{tex} \frac { 4 } { 3 } {/tex}

D

{tex} \frac { 1 } { 8 } {/tex}

Explanation



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Q 20. The value of the expression [cosec {tex} \left( 75 ^ { \circ } + \theta \right) {/tex} {tex} \left. - \sec \left( 15 ^ { \circ } - \theta \right) - \tan \left( 55 ^ { \circ } + \theta \right) + \cot \left( 35 ^ { \circ } - \theta \right) \right] {/tex} is :

A

{tex} - 1 {/tex}

{tex} 0 {/tex}

C

{tex} 1 {/tex}

D

{tex} \frac { 3 } { 2 } {/tex}

Explanation

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Q 21. Given that {tex} \sin \theta = \frac { a } { b } {/tex} then {tex} \cos \theta {/tex} is equal to

A

{tex} \frac { b } { \sqrt { b ^ { 2 } - a ^ { 2 } } } {/tex}

B

{tex} \frac { b } { a } {/tex}

{tex} \frac { \sqrt { b ^ { 2 } - a ^ { 2 } } } { b } {/tex}

D

{tex} \frac { a } { \sqrt { b ^ { 2 } - a ^ { 2 } } } {/tex}

Explanation

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Q 22. The value of (tan {tex} \left. 1 ^ { \circ } \tan 2 ^ { \circ } \tan 3 ^ { \circ } \dots \tan 89 ^ { \circ } \right) {/tex} is :

A

{tex} { 0 } {/tex}

{tex}1{/tex}

C

{tex}2{/tex}

D

{tex} \frac { 1 } { 2 } {/tex}

Explanation

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Q 23. If {tex} \Delta A B C {/tex} is right angled at {tex} C , {/tex} then the value of {tex} \cos {/tex} {tex} ( A + B ) {/tex} is :

{tex} 0{/tex}

B

{tex} 1{/tex}

C

{tex} \frac { 1 } { 2 } {/tex}

D

{tex} \frac { \sqrt { 3 } } { 2 } {/tex}

Explanation

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Q 24. If {tex} \sin A + \sin ^ { 2 } A = 1 , {/tex} then the value of the expression {tex} \left( \cos ^ { 2 } A + \cos ^ { 4 } A \right) {/tex} is :

{tex} 1{/tex}

B

{tex} \frac { 1 } { 2 } {/tex}

C

{tex} 2{/tex}

D

{tex} 3{/tex}

Explanation


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Q 25. Given that {tex} \sin \alpha = \frac { 1 } { 2 } {/tex} and {tex} \cos \beta = \frac { 1 } { 2 } {/tex}, then the value of {tex} ( \alpha + \beta ) {/tex} is :

A

{tex} 0 ^ { \circ } {/tex}

B

{tex} 30 ^ { \circ } {/tex}

C

{tex} 60 ^ { \circ } {/tex}

{tex} 90 ^ { \circ } {/tex}

Explanation